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#!/usr/bin/env python
#
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 1997-2016 California Institute of Technology.
# Copyright (c) 2016-2025 The Uncertainty Quantification Foundation.
# License: 3-clause BSD. The full license text is available at:
# - https://github.com/uqfoundation/pathos/blob/master/LICENSE
"""
Chebyshev's polynomials
"""
from numpy import sum as numpysum
from numpy import asarray
from mystic.math import polyeval, poly1d
# coefficients for specific Chebyshev polynomials
chebyshev2coeffs = [2., 0., -1.]
chebyshev4coeffs = [8., 0., -8., 0., 1.]
chebyshev6coeffs = [32., 0., -48., 0., 18., 0., -1.]
chebyshev8coeffs = [128., 0., -256., 0., 160., 0., -32., 0., 1.]
chebyshev16coeffs = [32768., 0., -131072., 0., 212992., 0., -180224., 0., 84480., 0., -21504., 0., 2688., 0., -128., 0., 1]
def chebyshevcostfactory(target):
def chebyshevcost(trial,M=61):
"""The costfunction for order-n Chebyshev fitting.
M evaluation points between [-1, 1], and two end points"""
result=0.0
x=-1.0
dx = 2.0 / (M-1)
for i in range(M):
px = polyeval(trial, x)
if px<-1 or px>1:
result += (1 - px) * (1 - px)
x += dx
px = polyeval(trial, 1.2) - polyeval(target, 1.2)
if px<0: result += px*px
px = polyeval(trial, -1.2) - polyeval(target, -1.2)
if px<0: result += px*px
return result
return chebyshevcost
# prepared cost factories
chebyshev2cost = chebyshevcostfactory(chebyshev2coeffs)
chebyshev4cost = chebyshevcostfactory(chebyshev4coeffs)
chebyshev6cost = chebyshevcostfactory(chebyshev6coeffs)
chebyshev8cost = chebyshevcostfactory(chebyshev8coeffs)
chebyshev16cost = chebyshevcostfactory(chebyshev16coeffs)
# End of file
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